The dimensions of `(a)/(b)` in the equation `P= (a^(2)-t^(2))/(bx)` where P is pressure, x is distance and t is time are

Options

A. `[M^(2)LT^(-3)]`
B. `[ML^(0)T^(-2)]`
C. `[ML^(3)T^(-1)]`
D. `[M^(0)LT^(-3)]`

Answer

B

Explanation

`pP= (a-t^(2))/(bx)` Dimensions of `a= [T^(2)]` as `t^(2)` is subtracted from a.
From `P= (a-t^(2))/(bx)= (t^(2))/(bx)`
`:. [b]= ([t^(2)])/([Px])= ([T^(2)])/([ML^(-1)T^(-2)][L])= [M^(-1)L^(0)T^(4)]`
`:. [(a)/(b)]= ([T^(2)])/([M^(-1)L^(0)T^(4)])= [ML^(0)T^(-2)]`